# Question #bf123

##### 1 Answer

i) 2 loops

ii) 16 loops

#### Explanation:

The equation relating tension and speed of wave is given by:

*where: #T" is the tension"; mu" is the linear density of the string"#*

Since we know that

**I)Tension increased by a factor of 4**

Let

The string used is the same, thus the linear density,

The frequency of the vibrator is also kept as the same,

Rearranging

since

*subscript #i# for initial, #f# for final*

Therefore the number of loops formed will be 2.

**II)Frequency increased by a factor of 4**

Now, Tension instead of frequency becomes constant.

Since Tension and Linear density remain the same,

Thus,

Let

Thefore, the number of loops is 16.